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Segregation–rheology feedback in bidisperse granular flows: a coupled Stokes’ problem

Published online by Cambridge University Press:  25 March 2024

Tomás Trewhela Open the ORCID record for Tomás Trewhela [Opens in a new window]
Tomás Trewhela*
Affiliation:
Facultad de Ingeniería y Ciencias, Universidad Adolfo Ibañez, Av. Padre Hurtado 750, 2562340 Viña del Mar, Chile
*
†Email address for correspondence: [email protected]
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Abstract

The feedback between particle-size segregation and rheology in bidisperse granular flows is studied using the Stokes’ problem configuration. A method of lines scheme is implemented to solve the coupled momentum and segregation equations for a normally graded particle size distributed bulk at constant solids volume fraction. The velocity profiles develop quickly into a transient state, decoupled from segregation yet determined by the particle size. From this transient state, the velocity profile changes due to the particles’ relative movement, which redistributes the frictional response, hence its rheology. Additionally, the particles’ relative friction is modified via a frictional coefficient ratio, by analogy with the particles’ size ratio. While positive values of this coefficient exacerbate the nonlinearity of the velocity profiles induced by size differences, negative values dampen this behaviour. The numerical solutions reproduce well the analytical solutions for the velocity profile, which can be obtained from the steady-state conditions of the momentum and segregation equations for the transient and steady states, respectively. Segregation–momentum balances and four characteristic time scales can be established to propose two non-dimensional quantities, including specific Schmidt and Péclet numbers that describe broadly the segregation–rheology feedback. The proposed scheme, theoretical solutions and non-dimensional numbers offer a combined approach to understand segregation and flow dynamics within a granular bulk, extensible across many flow configurations.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 983 , 25 March 2024 , A45
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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Supplementary material: File

Trewhela supplementary movie 1

Small particle concentrations 𝜙𝑠 and velocity û profiles for various 𝜒𝑑 = {0.2, 0.5, 0.7} values (𝑅𝑑 = {1.25, 2, 3.33} respectively) considering 𝑢𝑤 = 0.2 m/s, 𝑝𝑤 = 100 Pa and 𝜇𝑤 = 0.5.
Download Trewhela supplementary movie 1(File)
File 8.2 MB
Supplementary material: File

Trewhela supplementary movie 2

Small particle concentrations 𝜙𝑠 and velocity û profiles for the initially-mixed conditions 𝜙0𝑠= {0.25, 0.5, 0.75} considering 𝑢𝑤 = 0.2 m/s, 𝑝𝑤 = 100 Pa, 𝜇𝑤 = 0.5 and 𝑅𝑑 = 3.33.
Download Trewhela supplementary movie 2(File)
File 8.2 MB
Supplementary material: File

Trewhela supplementary movie 3

Small particle concentration 𝜙𝑠 and various velocity û profiles for variable 𝜒𝜇 = {−0.03, −0.02, −0.01, 0, 0.01} considering 𝑢𝑤 = 0.2 m/s, 𝑝𝑤 = 300 Pa, 𝜇𝑤 = 0.5 and 𝑅𝑑 = 2.
Download Trewhela supplementary movie 3(File)
File 7.1 MB
Supplementary material: File

Trewhela supplementary movie 4

Temporal evolution of the velocity profile û for the 𝑅𝑑 = 2 and 𝜒𝜇 = −0.03 case compared with its corresponding transient (solid lines) and steady-state (dashed dot line) solutions.
Download Trewhela supplementary movie 4(File)
File 7.7 MB
Supplementary material: File

Trewhela supplementary movie 5

Temporal evolution of the velocity profile û for the 𝑅𝑑 = 2 and 𝜒𝜇 = −0.01 case compared with its corresponding transient (solid lines) and steady-state (dashed dot line) solutions.
Download Trewhela supplementary movie 5(File)
File 7.6 MB
Supplementary material: File

Trewhela supplementary movie 6

Temporal evolution of the velocity profile û for the 𝑅𝑑 = 2 and 𝜒𝜇 = 0.01 case compared with its corresponding transient (solid lines) and steady-state (dashed dot line) solutions.
Download Trewhela supplementary movie 6(File)
File 7.8 MB